Question: Simplify the following expression: $ n = \dfrac{1}{5z + 6} - \dfrac{1}{9} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{9}{9}$ $ \dfrac{1}{5z + 6} \times \dfrac{9}{9} = \dfrac{9}{45z + 54} $ Multiply the second expression by $\dfrac{5z + 6}{5z + 6}$ $ \dfrac{1}{9} \times \dfrac{5z + 6}{5z + 6} = \dfrac{5z + 6}{45z + 54} $ Therefore $ n = \dfrac{9}{45z + 54} - \dfrac{5z + 6}{45z + 54} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{9 - (5z + 6) }{45z + 54} $ Distribute the negative sign: $n = \dfrac{9 - 5z - 6}{45z + 54}$ $n = \dfrac{-5z + 3}{45z + 54}$